| Parameter | Base model |
|---|---|
| swang1 (RHC) | 1.16 [1.01, 1.32], p =0.030 |
| cat chf (Others) | 1.71 [1.29, 2.25], p <0.001 |
| age | 1.03 [1.03, 1.04], p <0.001 |
| Observations | 5733 |
Marginal effectsとその周辺
多変量回帰・・・好きですか？
2025-08-11
回帰分析について
皆さん多変量回帰は好きですか？
古くから研究されつくされており、信頼感がある
多くの統計ソフトに入っており、行うのが簡単
解釈性が高く、分かりやすい
本当？
多変量回帰は簡単？
Many regression species
- 多変量回帰は多くの種類がある
- 0/1でLogistic回帰
- 整数値だとPoisson回帰
- 順序ロジット
- Censored regression(Cox回帰もこのうち)
- 選択肢が多く、その分どうすればよいのか分からない！
例えば・・・・・・
- ICU入室患者に対してRHCが予後を改善するかをみた観察研究(Connors et al. 1996)
- Propensity scoreを広めた研究としても有名
- 例えば、RHCが半年以内の死亡と関連するかをロジスティック回帰で解析をする
- 結果として、RHCは半年以内の死亡と関連する！
- しかし、ここで上司からのつっこみ
上司からのつっこみ①
結果①
| Parameter | Base model | Interact model |
|---|---|---|
| swang1 (RHC) | 1.16 [1.01, 1.32], p =0.030 | 1.52 [1.02, 2.26], p =0.041 |
| cat chf (Others) | 1.71 [1.29, 2.25], p <0.001 | 1.94 [1.40, 2.69], p <0.001 |
| age | 1.03 [1.03, 1.04], p <0.001 | 1.03 [1.03, 1.04], p <0.001 |
| swang1 (RHC) × cat chf (Others) | 0.74 [0.49, 1.12], p =0.158 | |
| Observations | 5733 | 5733 |
上司からのつっこみ②
結果②
| Parameter | Base model | Interact model | Spline model |
|---|---|---|---|
| swang1 (RHC) | 1.16 [1.01, 1.32], p =0.030 | 1.52 [1.02, 2.26], p =0.041 | 1.49 [1.00, 2.23], p =0.049 |
| cat chf (Others) | 1.71 [1.29, 2.25], p <0.001 | 1.94 [1.40, 2.69], p <0.001 | 1.94 [1.40, 2.70], p <0.001 |
| age | 1.03 [1.03, 1.04], p <0.001 | 1.03 [1.03, 1.04], p <0.001 | |
| swang1 (RHC) × cat chf (Others) | 0.74 [0.49, 1.12], p =0.158 | 0.75 [0.49, 1.14], p =0.172 | |
| rcs(age ( degree) | 0.99 [0.96, 1.01], p =0.325 | ||
| rcs(age ( degree) | 1.04 [0.89, 1.21], p =0.611 | ||
| rcs(age ( degree) | 1.04 [1.03, 1.05], p <0.001 | ||
| Observations | 5733 | 5733 | 5733 |
最終的に・・・・・・
例えば、2つの連続値をSplineで表したの場合
- 解釈・・・・・・
我々はどこにいる？
こんな時にJAMA！
- “誰に”、“どの統計量で”計測するのか？
- Causal Estimandを決める (Dahabreh and Bibbins-Domingo 2024)
我々(臨床医)のしたい事
- 根本的な問いかけ
- 「誰への治療効果ですか？」
- 「どうやった時の治療効果ですか？」
線形回帰の係数だと駄目な理由は？
- 線形回帰の係数の解釈 = 条件付き期待値
- 他の値を固定した時に、その因子を1単位変化した時の平均的なアウトカムの変化量
- その結果、係数(OR, HRなど)という1つの値にまるめてしまう
- 複雑な関係性をこの係数のみを報告する事で逆にわかりにくくなる事もある
- Ex. HFmrEFとHFrEFでARNIの効果が変わる
じゃあ、どうやって報告する？
- 「誰に？」「何が？」「どのくらい？」変化したら、アウトカムが変化するか？
- 難しい言葉でいうと“Estimand”を報告する必要がある
- 例えば
- 群全体: ATE
- 治療を受けた群全体: ATT
- 治療を受けなかった群全体: ATU
ここまでの纏め
- 多変量解析は解釈がわかりにくい！
- 特に、InteractionやSplineが入るとよりわかりにくい
- 通常の解析だと、結果は集団全体の平均で丸め込まれてしまう
- Estimandをどうやって出せばいい？
Standardizationあるいは prametric g-formulaの基礎
Marginal effectsという選択肢
- G-computationを用いて限界効果を出す手法
- 本来は、結果のStandardizationの手法
- Estimandを決定する方法でもある(Hernan 2024)
G-computationの考え方
実践①
- 生データ
# A tibble: 5,733 × 6
rowid swang1 estimate conf.low conf.high death_01
<int> <chr> <dbl> <dbl> <dbl> <dbl>
1 1 No RHC 0.606 0.535 0.672 0
2 2 RHC 0.839 0.787 0.880 1
3 3 RHC 0.743 0.675 0.801 0
4 4 No RHC 0.746 0.684 0.800 1
5 5 RHC 0.872 0.830 0.904 1
6 6 No RHC 0.780 0.721 0.829 0
7 7 No RHC 0.585 0.519 0.648 0
8 8 No RHC 0.287 0.231 0.350 1
9 9 No RHC 0.315 0.247 0.394 0
10 10 RHC 0.593 0.535 0.648 0
# ℹ 5,723 more rows- 元データ+swang1列のみ変更して複製したデータセット
# A tibble: 11,466 × 6
rowid swang1 estimate conf.low conf.high death_01
<int> <chr> <dbl> <dbl> <dbl> <dbl>
1 1 No RHC 0.606 0.535 0.672 0
2 2 No RHC 0.823 0.768 0.868 1
3 3 No RHC 0.721 0.651 0.782 0
4 4 No RHC 0.746 0.684 0.800 1
5 5 No RHC 0.859 0.815 0.893 1
6 6 No RHC 0.780 0.721 0.829 0
7 7 No RHC 0.585 0.519 0.648 0
8 8 No RHC 0.287 0.231 0.350 1
9 9 No RHC 0.315 0.247 0.394 0
10 10 No RHC 0.567 0.508 0.623 0
# ℹ 11,456 more rows- 行数が2倍(5733→11466)になっている事に注意！
実践②
swang1 Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
No RHC 0.638 0.00792 80.5 <0.001 Inf 0.623 0.654
RHC 0.666 0.01034 64.4 <0.001 Inf 0.645 0.686
Type: response- swang1毎でのestimateを纏める
- 差をとったらRisk differenceを出せる
- この結果を変形する事で色々な数値を出せる。
実践③
Risk ratio
Estimate Pr(>|z|) S 2.5 % 97.5 %
1.04 0.0433 4.5 1 1.09
Term: swang1
Type: response
Comparison: ln(mean(RHC) / mean(No RHC))Odds ratio
Estimate Pr(>|z|) S 2.5 % 97.5 %
1.13 0.0454 4.5 1 1.27
Term: swang1
Type: response
Comparison: ln(odds(RHC) / odds(No RHC))- 疫学的にはリスク差(あるいはリスク比)が最も知りたい数値
- Odds ratioは発生率が低いイベントでないと、Risk ratioと近似出来ない(Cummings 2009)
G-computtionの応用
G-computationの応用～ATE/ATT/ATU
- 元データのうち、元々Interventionが0/1の群だけで同様の事をするとATT/ATUも推定可能
- Interventionだけでなくても、興味がある変数を動かす事で周辺効果(marginal effect)を出すことが可能
実践④
- 例えば、患者背景がCHFでRHCの効果がどうなるかをみたい時
# A tibble: 10,554 × 7
rowid swang1 cat_chf estimate conf.low conf.high death_01
<int> <chr> <chr> <dbl> <dbl> <dbl> <dbl>
1 1 No RHC Others 0.606 0.535 0.672 0
2 2 No RHC Others 0.823 0.768 0.868 1
3 3 No RHC Others 0.721 0.651 0.782 0
4 4 No RHC Others 0.746 0.684 0.800 1
5 5 No RHC Others 0.859 0.815 0.893 1
6 6 No RHC Others 0.780 0.721 0.829 0
7 7 No RHC Others 0.585 0.519 0.648 0
8 8 No RHC Others 0.287 0.231 0.350 1
9 9 No RHC Others 0.315 0.247 0.394 0
10 10 No RHC Others 0.567 0.508 0.623 0
# ℹ 10,544 more rows
swang1 Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
No RHC 0.562 0.0306 18.3 <0.001 247.4 0.502 0.622
RHC 0.651 0.0317 20.5 <0.001 307.8 0.588 0.713
Type: response- まずは、原疾患が心不全以外の患者を抜粋
- RHCのみ0と1両者でそれ以外の列を複製したデータセットを作成
- RHC毎の死亡率を計算
# A tibble: 456 × 6
swang1 cat_chf estimate conf.low conf.high death_01
<chr> <chr> <dbl> <dbl> <dbl> <dbl>
1 RHC CHF 0.0967 0.000843 0.193 1
2 No RHC CHF 0.0904 0.00145 0.179 1
3 No RHC CHF 0.0793 0.00122 0.157 0
4 No RHC CHF 0.0945 0.000226 0.189 1
5 No RHC CHF 0.100 0.00131 0.199 0
6 No RHC CHF 0.0998 0.00141 0.198 0
7 No RHC CHF 0.0954 0.00136 0.189 1
8 RHC CHF 0.0949 0.00119 0.189 0
9 No RHC CHF 0.0919 0.00161 0.182 1
10 No RHC CHF 0.0816 0.000612 0.163 1
# ℹ 446 more rows
Estimate Pr(>|z|) S 2.5 % 97.5 %
1.16 0.0474 4.4 1 1.34
Term: swang1
Type: response
Comparison: ln(mean(RHC) / mean(No RHC))- CHFの患者のみ抜き出し、回帰モデルを元にRHCとNo RHCのRiskの差を一人ずつ計算を計算する
- 平均して1つの数値を出す
G-computationの応用～Propensity score match
- Propensity score matchを計算
- Matched cohortを作成(仮想Randomized？)
- 残った
- どの群を選ぶかでATT/ATE/ATUも簡単に計算可能！(Greifer 2025)
実践⑤～準備
- まずはPropensity score match行う
- Matched dataを出す
- Propensity scoreに用いた共変量を含めてアウトカムの回帰モデルを作成する
- この重みも用いることに注意！
A `matchit` object
- method: 1:1 nearest neighbor matching without replacement
- distance: Propensity score
- estimated with logistic regression
- number of obs.: 5733 (original), 4366 (matched)
- target estimand: ATT
- covariates: cat_chf, age, sex, race, edu, income, wtkilo1, temp1, meanbp1, resp1, hrt1, pafi1, paco21, ph1, wblc1, hema1, sod1, pot1, crea1, bili1, alb1, cardiohx, chfhx, immunhx, transhx, amihxmatched data # A tibble: 4,366 × 6
death_yn swang1 cat_chf age distance weights
<dbl> <chr> <chr> <dbl> <dbl> <dbl>
1 0 No RHC Others 70.3 0.502 1
2 1 RHC Others 78.2 0.563 1
3 0 RHC Others 46.1 0.402 1
4 1 No RHC Others 75.3 0.344 1
5 1 RHC Others 67.9 0.302 1
6 0 No RHC Others 55.0 0.379 1
7 1 No RHC Others 43.6 0.281 1
8 0 No RHC Others 18.0 0.283 1
9 0 RHC Others 48.4 0.490 1
10 0 No RHC Others 34.4 0.393 1
# ℹ 4,356 more rowsアウトカムモデル
Call:
glm(formula = death_01 ~ swang1 * cat_chf + rcs(age, 4) + crea1 +
sex + race + edu + income + wtkilo1 + temp1 + meanbp1 + resp1 +
hrt1 + pafi1 + paco21 + ph1 + wblc1 + hema1 + sod1 + pot1 +
bili1 + alb1 + cardiohx + chfhx + immunhx + transhx + amihx,
family = binomial, data = dat_m, weights = weights)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 8.3720758 3.0519820 2.743 0.006085 **
swang1RHC 0.2979878 0.2142302 1.391 0.164234
cat_chfOthers 0.6272870 0.1929188 3.252 0.001148 **
rcs(age, 4)age 0.0460262 0.0073111 6.295 3.07e-10 ***
rcs(age, 4)age' -0.0300047 0.0153201 -1.959 0.050169 .
rcs(age, 4)age'' 0.1399522 0.0931435 1.503 0.132957
crea1 0.0105633 0.0179507 0.588 0.556221
sexMale 0.2461617 0.0722525 3.407 0.000657 ***
raceother 0.1766005 0.1651406 1.069 0.284892
racewhite 0.0327267 0.0998068 0.328 0.742987
edu 0.0143607 0.0127289 1.128 0.259236
income$11-$25k 0.0940105 0.1417030 0.663 0.507053
income$25-$50k -0.0403601 0.1402408 -0.288 0.773506
incomeUnder $11k 0.3384458 0.1377695 2.457 0.014026 *
wtkilo1 -0.0051664 0.0013121 -3.937 8.23e-05 ***
temp1 -0.0980770 0.0211773 -4.631 3.63e-06 ***
meanbp1 -0.0033602 0.0009997 -3.361 0.000776 ***
resp1 0.0063613 0.0025859 2.460 0.013895 *
hrt1 0.0028575 0.0009159 3.120 0.001809 **
pafi1 0.0005013 0.0003571 1.404 0.160424
paco21 0.0004425 0.0038424 0.115 0.908323
ph1 -1.0754772 0.3902359 -2.756 0.005852 **
wblc1 0.0015517 0.0028332 0.548 0.583905
hema1 -0.0201725 0.0049354 -4.087 4.36e-05 ***
sod1 0.0034946 0.0046319 0.754 0.450575
pot1 0.0548594 0.0369037 1.487 0.137132
bili1 0.0572166 0.0093037 6.150 7.75e-10 ***
alb1 0.0149816 0.0517212 0.290 0.772075
cardiohx 0.0058533 0.1012471 0.058 0.953898
chfhx 0.4574501 0.1187363 3.853 0.000117 ***
immunhx 0.2341199 0.0796956 2.938 0.003307 **
transhx -0.3824780 0.0967037 -3.955 7.65e-05 ***
amihx -0.3281233 0.1715791 -1.912 0.055828 .
swang1RHC:cat_chfOthers -0.2139280 0.2264226 -0.945 0.344752
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 5552.0 on 4365 degrees of freedom
Residual deviance: 5064.5 on 4332 degrees of freedom
AIC: 5132.5
Number of Fisher Scoring iterations: 4実践⑤～結果
# A tibble: 4,366 × 8
rowid contrast estimate conf.low conf.high death_01 swang1 weights
<int> <chr> <dbl> <dbl> <dbl> <dbl> <chr> <dbl>
1 1 RHC - No RHC 0.0196 -0.0137 0.0529 0 No RHC 1
2 2 RHC - No RHC 0.0120 -0.00850 0.0324 1 RHC 1
3 3 RHC - No RHC 0.0163 -0.0115 0.0441 0 RHC 1
4 4 RHC - No RHC 0.0156 -0.0110 0.0422 1 No RHC 1
5 5 RHC - No RHC 0.00965 -0.00700 0.0263 1 RHC 1
6 6 RHC - No RHC 0.0193 -0.0134 0.0519 0 No RHC 1
7 7 RHC - No RHC 0.0169 -0.0120 0.0458 1 No RHC 1
8 8 RHC - No RHC 0.0177 -0.0126 0.0480 0 No RHC 1
9 9 RHC - No RHC 0.0201 -0.0140 0.0543 0 RHC 1
10 10 RHC - No RHC 0.0197 -0.0139 0.0533 0 No RHC 1
# ℹ 4,356 more rowsここから計算する
Estimate Pr(>|z|) S 2.5 % 97.5 %
1.03 0.122 3.0 0.992 1.07
Term: swang1
Type: response
Comparison: ln(mean(RHC) / mean(No RHC))# A tibble: 2,183 × 8
rowid contrast estimate conf.low conf.high death_01 swang1 weights
<int> <chr> <dbl> <dbl> <dbl> <dbl> <chr> <dbl>
1 1 RHC - No RHC 0.0120 -0.00850 0.0324 1 RHC 1
2 2 RHC - No RHC 0.0163 -0.0115 0.0441 0 RHC 1
3 3 RHC - No RHC 0.00965 -0.00700 0.0263 1 RHC 1
4 4 RHC - No RHC 0.0201 -0.0140 0.0543 0 RHC 1
5 5 RHC - No RHC 0.0207 -0.0145 0.0560 0 RHC 1
6 6 RHC - No RHC 0.0199 -0.0140 0.0538 1 RHC 1
7 7 RHC - No RHC 0.00868 -0.00604 0.0234 1 RHC 1
8 8 RHC - No RHC 0.0165 -0.0115 0.0446 1 RHC 1
9 9 RHC - No RHC 0.0146 -0.0106 0.0399 0 RHC 1
10 10 RHC - No RHC 0.0206 -0.0143 0.0556 1 RHC 1
# ℹ 2,173 more rowsここから計算する
Estimate Pr(>|z|) S 2.5 % 97.5 %
1.03 0.121 3.0 0.992 1.07
Term: swang1
Type: response
Comparison: ln(mean(RHC) / mean(No RHC))# A tibble: 2,183 × 8
rowid contrast estimate conf.low conf.high death_01 swang1 weights
<int> <chr> <dbl> <dbl> <dbl> <dbl> <chr> <dbl>
1 1 RHC - No RHC 0.0196 -0.0137 0.0529 0 No RHC 1
2 2 RHC - No RHC 0.0156 -0.0110 0.0422 1 No RHC 1
3 3 RHC - No RHC 0.0193 -0.0134 0.0519 0 No RHC 1
4 4 RHC - No RHC 0.0169 -0.0120 0.0458 1 No RHC 1
5 5 RHC - No RHC 0.0177 -0.0126 0.0480 0 No RHC 1
6 6 RHC - No RHC 0.0197 -0.0139 0.0533 0 No RHC 1
7 7 RHC - No RHC 0.0210 -0.0146 0.0565 1 No RHC 1
8 8 RHC - No RHC 0.0203 -0.0143 0.0550 0 No RHC 1
9 9 RHC - No RHC 0.0124 -0.00937 0.0342 0 No RHC 1
10 10 RHC - No RHC 0.0642 -0.0284 0.157 1 No RHC 1
# ℹ 2,173 more rowsここから計算する
Estimate Pr(>|z|) S 2.5 % 97.5 %
1.03 0.123 3.0 0.992 1.07
Term: swang1
Type: response
Comparison: ln(mean(RHC) / mean(No RHC))G-computationの応用～Doubly robust
- Propensity score weightingを計算
- Outcomeを目標とする多変量回帰を作成
- 上記を組み合わせてDoubly robustを計算可能
- どの群を選ぶかでATT/ATE/ATUも簡単に計算可能！
実践⑤～結果
A weightit object
- method: "glm" (propensity score weighting with GLM)
- number of obs.: 5733
- sampling weights: none
- treatment: 2-category
- estimand: ATE
- covariates: cat_chf, age, sex, race, edu, income, wtkilo1, temp1, meanbp1, resp1, hrt1, pafi1, paco21, ph1, wblc1, hema1, sod1, pot1, crea1, bili1, alb1, cardiohx, chfhx, immunhx, transhx, amihx# A tibble: 5,733 × 8
death_01 swang_yn age sex race cat_chf crea1 weights
<dbl> <dbl> <dbl> <chr> <chr> <chr> <dbl> <dbl>
1 0 0 70.3 Male white Others 1.20 2.01
2 1 1 78.2 Female white Others 0.600 1.78
3 0 1 46.1 Female white Others 2.60 2.49
4 1 0 75.3 Female white Others 1.70 1.53
5 1 1 67.9 Male white Others 3.60 3.31
6 0 0 86.1 Female white Others 1.40 1.12
7 0 0 55.0 Male white Others 1 1.61
8 1 0 43.6 Male white Others 0.700 1.39
9 0 0 18.0 Female white Others 1.70 1.39
10 0 1 48.4 Female white Others 0.5 2.04
# ℹ 5,723 more rows
Call:
WeightIt::glm_weightit(formula = death_01 ~ swang1 * cat_chf +
rcs(age, 4) + crea1 + sex + race + edu + income + wtkilo1 +
temp1 + meanbp1 + resp1 + hrt1 + pafi1 + paco21 + ph1 + wblc1 +
hema1 + sod1 + pot1 + bili1 + alb1 + cardiohx + chfhx + immunhx +
transhx + amihx, data = rhc_prep, family = binomial, weightit = wout_ate)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 6.2431313 3.1407162 1.988 0.046833 *
swang1RHC 0.4213975 0.2232617 1.887 0.059098 .
cat_chfOthers 0.5554860 0.1934359 2.872 0.004083 **
rcs(age, 4)age 0.0387122 0.0081293 4.762 1.92e-06 ***
rcs(age, 4)age' -0.0153697 0.0165989 -0.926 0.354474
rcs(age, 4)age'' 0.0599765 0.0973430 0.616 0.537805
crea1 0.0131695 0.0211148 0.624 0.532819
sexMale 0.2002275 0.0756056 2.648 0.008089 **
raceother 0.1047433 0.1674566 0.625 0.531646
racewhite -0.0776023 0.1063510 -0.730 0.465585
edu 0.0280096 0.0128521 2.179 0.029303 *
income$11-$25k 0.2348404 0.1495633 1.570 0.116375
income$25-$50k -0.0426852 0.1499175 -0.285 0.775855
incomeUnder $11k 0.4149254 0.1478977 2.805 0.005024 **
wtkilo1 -0.0032067 0.0014755 -2.173 0.029760 *
temp1 -0.0830270 0.0228051 -3.641 0.000272 ***
meanbp1 -0.0034465 0.0010272 -3.355 0.000793 ***
resp1 0.0038987 0.0026314 1.482 0.138445
hrt1 0.0029678 0.0009275 3.200 0.001375 **
pafi1 0.0005517 0.0003901 1.414 0.157261
paco21 -0.0042080 0.0037603 -1.119 0.263106
ph1 -0.7636761 0.3988971 -1.914 0.055560 .
wblc1 0.0007086 0.0029638 0.239 0.811040
hema1 -0.0259974 0.0052143 -4.986 < 1e-06 ***
sod1 0.0015924 0.0046547 0.342 0.732264
pot1 0.0750655 0.0403091 1.862 0.062568 .
bili1 0.0595551 0.0105584 5.641 < 1e-06 ***
alb1 -0.0196740 0.0551163 -0.357 0.721126
cardiohx -0.0686531 0.1058839 -0.648 0.516739
chfhx 0.5082114 0.1241712 4.093 4.26e-05 ***
immunhx 0.2218184 0.0795369 2.789 0.005289 **
transhx -0.3666306 0.0984877 -3.723 0.000197 ***
amihx -0.1936546 0.1720359 -1.126 0.260308
swang1RHC:cat_chfOthers -0.2871238 0.2391748 -1.200 0.229954
Standard error: HC0 robust (adjusted for estimation of weights)Risk ratio and 95% confidence interval
Estimate Pr(>|z|) S 2.5 % 97.5 %
1.05 0.0291 5.1 1 1.1
Term: swang1
Type: probs
Comparison: ln(mean(RHC) / mean(No RHC))A weightit object
- method: "glm" (propensity score weighting with GLM)
- number of obs.: 5733
- sampling weights: none
- treatment: 2-category
- estimand: ATT (focal: 1)
- covariates: cat_chf, age, sex, race, edu, income, wtkilo1, temp1, meanbp1, resp1, hrt1, pafi1, paco21, ph1, wblc1, hema1, sod1, pot1, crea1, bili1, alb1, cardiohx, chfhx, immunhx, transhx, amihx# A tibble: 5,733 × 8
death_01 swang_yn age sex race cat_chf crea1 weights
<dbl> <dbl> <dbl> <chr> <chr> <chr> <dbl> <dbl>
1 0 0 70.3 Male white Others 1.20 1.01
2 1 1 78.2 Female white Others 0.600 1
3 0 1 46.1 Female white Others 2.60 1
4 1 0 75.3 Female white Others 1.70 0.526
5 1 1 67.9 Male white Others 3.60 1
6 0 0 86.1 Female white Others 1.40 0.117
7 0 0 55.0 Male white Others 1 0.611
8 1 0 43.6 Male white Others 0.700 0.392
9 0 0 18.0 Female white Others 1.70 0.394
10 0 1 48.4 Female white Others 0.5 1
# ℹ 5,723 more rows
Call:
WeightIt::glm_weightit(formula = death_01 ~ swang1 * cat_chf +
rcs(age, 4) + crea1 + sex + race + edu + income + wtkilo1 +
temp1 + meanbp1 + resp1 + hrt1 + pafi1 + paco21 + ph1 + wblc1 +
hema1 + sod1 + pot1 + bili1 + alb1 + cardiohx + chfhx + immunhx +
transhx + amihx, data = rhc_prep, family = binomial, weightit = wout_att)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 8.6468892 3.2275906 2.679 0.007383 **
swang1RHC 0.2313120 0.2461137 0.940 0.347290
cat_chfOthers 0.5490938 0.2382303 2.305 0.021173 *
rcs(age, 4)age 0.0487811 0.0077472 6.297 < 1e-06 ***
rcs(age, 4)age' -0.0297895 0.0165337 -1.802 0.071585 .
rcs(age, 4)age'' 0.1139380 0.1052456 1.083 0.278990
crea1 0.0060007 0.0246616 0.243 0.807755
sexMale 0.2465548 0.0769534 3.204 0.001356 **
raceother 0.0313990 0.1767677 0.178 0.859015
racewhite -0.1276454 0.1069158 -1.194 0.232522
edu 0.0269046 0.0133725 2.012 0.044227 *
income$11-$25k -0.0033263 0.1483589 -0.022 0.982112
income$25-$50k -0.0861141 0.1484533 -0.580 0.561864
incomeUnder $11k 0.2440442 0.1463484 1.668 0.095404 .
wtkilo1 -0.0061903 0.0015972 -3.876 0.000106 ***
temp1 -0.0861481 0.0229575 -3.753 0.000175 ***
meanbp1 -0.0034707 0.0010540 -3.293 0.000991 ***
resp1 0.0066936 0.0028555 2.344 0.019074 *
hrt1 0.0023754 0.0010015 2.372 0.017702 *
pafi1 0.0005454 0.0004103 1.329 0.183791
paco21 -0.0035279 0.0037666 -0.937 0.348952
ph1 -1.1114260 0.4016787 -2.767 0.005658 **
wblc1 0.0024665 0.0027953 0.882 0.377565
hema1 -0.0214227 0.0053264 -4.022 5.77e-05 ***
sod1 0.0026557 0.0048592 0.547 0.584699
pot1 0.0727514 0.0415130 1.752 0.079688 .
bili1 0.0604808 0.0107892 5.606 < 1e-06 ***
alb1 -0.0395979 0.0546219 -0.725 0.468485
cardiohx 0.0564933 0.1115853 0.506 0.612661
chfhx 0.4867779 0.1401276 3.474 0.000513 ***
immunhx 0.2014825 0.0875316 2.302 0.021345 *
transhx -0.3366241 0.1055305 -3.190 0.001424 **
amihx -0.3235800 0.1851544 -1.748 0.080529 .
swang1RHC:cat_chfOthers -0.1254310 0.2589720 -0.484 0.628143
Standard error: HC0 robust (adjusted for estimation of weights)Risk ratio and 95% confidence interval
Estimate Pr(>|z|) S 2.5 % 97.5 %
1.04 0.115 3.1 0.991 1.08
Term: swang1
Type: probs
Comparison: ln(mean(RHC) / mean(No RHC))A weightit object
- method: "glm" (propensity score weighting with GLM)
- number of obs.: 5733
- sampling weights: none
- treatment: 2-category
- estimand: ATC (focal: 0)
- covariates: cat_chf, age, sex, race, edu, income, wtkilo1, temp1, meanbp1, resp1, hrt1, pafi1, paco21, ph1, wblc1, hema1, sod1, pot1, crea1, bili1, alb1, cardiohx, chfhx, immunhx, transhx, amihx# A tibble: 5,733 × 8
death_01 swang_yn age sex race cat_chf crea1 weights
<dbl> <dbl> <dbl> <chr> <chr> <chr> <dbl> <dbl>
1 0 0 70.3 Male white Others 1.20 1
2 1 1 78.2 Female white Others 0.600 0.777
3 0 1 46.1 Female white Others 2.60 1.49
4 1 0 75.3 Female white Others 1.70 1
5 1 1 67.9 Male white Others 3.60 2.31
6 0 0 86.1 Female white Others 1.40 1
7 0 0 55.0 Male white Others 1 1
8 1 0 43.6 Male white Others 0.700 1
9 0 0 18.0 Female white Others 1.70 1
10 0 1 48.4 Female white Others 0.5 1.04
# ℹ 5,723 more rows
Call:
WeightIt::glm_weightit(formula = death_01 ~ swang1 * cat_chf +
rcs(age, 4) + crea1 + sex + race + edu + income + wtkilo1 +
temp1 + meanbp1 + resp1 + hrt1 + pafi1 + paco21 + ph1 + wblc1 +
hema1 + sod1 + pot1 + bili1 + alb1 + cardiohx + chfhx + immunhx +
transhx + amihx, data = rhc_prep, family = binomial, weightit = wout_atc)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 4.2139813 3.7473840 1.125 0.260796
swang1RHC 0.5771091 0.2328870 2.478 0.013210 *
cat_chfOthers 0.5915078 0.1898688 3.115 0.001837 **
rcs(age, 4)age 0.0332256 0.0093838 3.541 0.000399 ***
rcs(age, 4)age' -0.0074427 0.0190591 -0.391 0.696162
rcs(age, 4)age'' 0.0298757 0.1088120 0.275 0.783653
crea1 0.0224478 0.0225776 0.994 0.320099
sexMale 0.1741977 0.0861000 2.023 0.043052 *
raceother 0.1419371 0.1843876 0.770 0.441433
racewhite -0.0438198 0.1221636 -0.359 0.719821
edu 0.0285804 0.0145419 1.965 0.049369 *
income$11-$25k 0.3960766 0.1745643 2.269 0.023272 *
income$25-$50k -0.0135415 0.1768372 -0.077 0.938961
incomeUnder $11k 0.5366253 0.1729339 3.103 0.001915 **
wtkilo1 -0.0017586 0.0016487 -1.067 0.286118
temp1 -0.0796040 0.0263993 -3.015 0.002567 **
meanbp1 -0.0033540 0.0011348 -2.956 0.003121 **
resp1 0.0021765 0.0029054 0.749 0.453777
hrt1 0.0033948 0.0010413 3.260 0.001114 **
pafi1 0.0005489 0.0004467 1.229 0.219155
paco21 -0.0036611 0.0041598 -0.880 0.378800
ph1 -0.4927880 0.4780367 -1.031 0.302607
wblc1 -0.0004794 0.0037160 -0.129 0.897355
hema1 -0.0280287 0.0059791 -4.688 2.76e-06 ***
sod1 0.0006330 0.0052550 0.120 0.904116
pot1 0.0763670 0.0467941 1.632 0.102684
bili1 0.0586712 0.0118855 4.936 < 1e-06 ***
alb1 -0.0068194 0.0650514 -0.105 0.916510
cardiohx -0.1621082 0.1189444 -1.363 0.172917
chfhx 0.5165472 0.1373658 3.760 0.000170 ***
immunhx 0.2322479 0.0877537 2.647 0.008131 **
transhx -0.3913542 0.1102084 -3.551 0.000384 ***
amihx -0.0822611 0.1879259 -0.438 0.661581
swang1RHC:cat_chfOthers -0.4241877 0.2533146 -1.675 0.094023 .
Standard error: HC0 robust (adjusted for estimation of weights)Risk ratio and 95% confidence interval
Estimate Pr(>|z|) S 2.5 % 97.5 %
1.06 0.0271 5.2 1.01 1.12
Term: swang1
Type: probs
Comparison: ln(mean(RHC) / mean(No RHC))G-computationの応用～機械学習を用いた手法
- 厳密にはStandardizationとは違うが・・・・・・
- Datasetを倍にして機械学習で推定する方法をS-learnerという
- 因果推定を行う場合は、重み付けも行うD-learnerやX-learnerもある
- 信頼区間やP値が出せないのが難点
実践⑤ モデル作成
モデルの中身══ Workflow [trained] ══════════════════════════════════════════════════════════
Preprocessor: Variables
Model: boost_tree()
── Preprocessor ────────────────────────────────────────────────────────────────
Outcomes: death_01
Predictors: c("age", "crea1", "edu", "wtkilo1", "temp1", "meanbp1", "resp1",
"hrt1", "pafi1", "paco21", "ph1", "wblc1", "hema1", "sod1",
"pot1", "bili1", "alb1", "cardiohx", "chfhx", "immunhx",
"transhx", "amihx", "swang1_RHC", "cat_chf_Others", "cat1_CHF",
"cat1_Cirrhosis", "cat1_Colon.Cancer", "cat1_Coma", "cat1_COPD",
"cat1_Lung.Cancer", "cat1_MOSF.w.Malignancy", "cat1_MOSF.w.Sepsis",
"sex_Male", "race_other", "race_white", "income_X.11..25k",
"income_X.25..50k", "income_Under..11k")
── Model ───────────────────────────────────────────────────────────────────────
##### xgb.Booster
raw: 51.4 Kb
call:
xgboost::xgb.train(params = list(eta = 0.3, max_depth = 6, gamma = 0,
colsample_bytree = 1, colsample_bynode = 1, min_child_weight = 1,
subsample = 1), data = x$data, nrounds = 15, watchlist = x$watchlist,
verbose = 0, nthread = 1, objective = "binary:logistic")
params (as set within xgb.train):
eta = "0.3", max_depth = "6", gamma = "0", colsample_bytree = "1", colsample_bynode = "1", min_child_weight = "1", subsample = "1", nthread = "1", objective = "binary:logistic", validate_parameters = "TRUE"
xgb.attributes:
niter
callbacks:
cb.evaluation.log()
# of features: 38
niter: 15
nfeatures : 38
evaluation_log:
iter training_logloss
<num> <num>
1 0.6358522
2 0.6015622
--- ---
14 0.4678196
15 0.4606318実践⑤ 仮想データ作成
# A tibble: 11,466 × 32
rowidcf death_yn death_days swang_yn cat_chf cat1 age crea1 sex race
<int> <dbl> <dbl> <dbl> <chr> <chr> <dbl> <dbl> <chr> <chr>
1 1 0 180 0 Others COPD 70.3 1.20 Male white
2 2 1 45 1 Others MOSF w/… 78.2 0.600 Fema… white
3 3 0 180 1 Others MOSF w/… 46.1 2.60 Fema… white
4 4 1 37 0 Others ARF 75.3 1.70 Fema… white
5 5 1 2 1 Others MOSF w/… 67.9 3.60 Male white
6 6 0 180 0 Others COPD 86.1 1.40 Fema… white
7 7 0 180 0 Others MOSF w/… 55.0 1 Male white
8 8 1 38 0 Others ARF 43.6 0.700 Male white
9 9 0 180 0 Others MOSF w/… 18.0 1.70 Fema… white
10 10 0 180 1 Others ARF 48.4 0.5 Fema… white
# ℹ 11,456 more rows
# ℹ 22 more variables: edu <dbl>, income <chr>, wtkilo1 <dbl>, temp1 <dbl>,
# meanbp1 <dbl>, resp1 <dbl>, hrt1 <int>, pafi1 <dbl>, paco21 <dbl>,
# ph1 <dbl>, wblc1 <dbl>, hema1 <dbl>, sod1 <int>, pot1 <dbl>, bili1 <dbl>,
# alb1 <dbl>, cardiohx <int>, chfhx <int>, immunhx <int>, transhx <int>,
# amihx <int>, swang1 <chr>実践⑤ 仮想データ作成
# A tibble: 11,466 × 4
swang1 death_01 probability_1 predicted_class
<chr> <fct> <dbl> <fct>
1 No RHC 0 0.536 1
2 No RHC 1 0.737 1
3 No RHC 0 0.570 1
4 No RHC 1 0.628 1
5 No RHC 1 0.726 1
6 No RHC 0 0.732 1
7 No RHC 0 0.531 1
8 No RHC 1 0.253 0
9 No RHC 0 0.369 0
10 No RHC 0 0.400 0
# ℹ 11,456 more rows# A tibble: 2 × 2
swang1 mean_death_prob
<chr> <dbl>
1 No RHC 0.642
2 RHC 0.655G-computationの利点
- 「この集団の介入を変えたら、どの程度良くなるか？」をダイレクトに伝えられる(King, Tomz, and Wittenberg 2000)
- InteractionやSplineなど複雑な式でもシンプルに結果を伝えられる
- 予測と因果を両方行う事が可能！
予測～Average marginal prediction
- 通常のアウトカム式のみで一発勝負 ここはDoubly robustは使っちゃいけない
因果～Average comparison
- AIPWやTLMEを使った方が安心かもしれない
- ただし、効率が悪い可能性もあり・・・・・・
G-computationでのAdvancedな統計結果の伝え方
- 伝えるEstimandを正確に伝える
- 「誰に」、「もし＊＊したら」、「平均的にどのような効果？」が「どれくらいの確実性」あるかを言う
- 出来るだけ、臨床的に意味がある差かどうかを考える
G-computationの限界
- 基本的には通常の回帰と一緒
- Unobserved confoundingやMisspecificationに弱い
- 予測の為ではなく因果よりと考えたほうが良い
- モデル作成でStep wiseや機械学習のようなやり方はしないほうが良い
最後に
Box先生の名言
すべてのモデルは誤っている。しかし、そのうちのいくつかは役に立つ。
RでのMarginal effectsの使い方
emmeans,marginaleffects,easystatsのmodelbasedなど- AIMの論文にも記載があり使いやすいのは
marginaleffects
Thank you for your listening!!
References
Connors, A F, Jr, T Speroff, N V Dawson, C Thomas, F E Harrell Jr, D Wagner, N Desbiens, et al. 1996. “The Effectiveness of Right Heart Catheterization in the Initial Care of Critically Ill Patients. SUPPORT Investigators.” JAMA: The Journal of the American Medical Association 276 (11): 889–97. https://doi.org/10.1001/jama.276.11.889.
Cummings, Peter. 2009. “The Relative Merits of Risk Ratios and Odds Ratios.” Archives of Pediatrics & Adolescent Medicine 163 (5): 438–45. https://doi.org/10.1001/archpediatrics.2009.31.
Dahabreh, Issa J, and Kirsten Bibbins-Domingo. 2024. “Causal Inference about the Effects of Interventions from Observational Studies in Medical Journals.” JAMA: The Journal of the American Medical Association 331 (21): 1845–53. https://doi.org/10.1001/jama.2024.7741.
Greifer, Noah. 2025. “Estimating Effects After Matching.” https://cran.r-project.org/web/packages/MatchIt/vignettes/estimating-effects.html.
Hernan, Miguel A. 2024. Causal Inference: What If. Edited by James M. Robins. Boca Raton: Taylor & Francis.
King, Gary, Michael Tomz, and Jason Wittenberg. 2000. “Making the Most of Statistical Analyses: Improving Interpretation and Presentation.” American Journal of Political Science 44 (2): 347–61. https://doi.org/10.2307/2669316.